Noise and disturbance in quantum measurements: an information-theoretic approach

Abstract

We introduce information-theoretic definitions for noise and disturbance in quantum measurements and prove a state-independent noise-disturbance tradeoff relation that these quantities have to satisfy in any conceivable setup. Contrary to previous approaches, the information-theoretic quantities we define are invariant under relabelling of outcomes, and allow for the possibility of using quantum or classical operations to `correct' for the disturbance. We also show how our bound implies strong tradeoff relations for mean square deviations.

v3: to appear on PRL (some issues fixed, supplemental material expanded). v2: replaced with submitted version; 5 two-column pages + 6 one-column pages + 3 figures; one issue corrected and few references added. v1: 17 pages, 3 figures

References in corpus (10)

• Proof of Heisenberg's error-disturbance relation
• Majorization entropic uncertainty relations
• How well can one jointly measure two incompatible observables on a given quantum state?
• Experimental Test of Error-Disturbance Uncertainty Relations by Weak Measurement
• Joint quantum measurements with minimum uncertainty
• Violation of Heisenberg's error-disturbance uncertainty relation in neutron spin measurements
• Global information balance in quantum measurements
• The information-theoretic costs of simulating quantum measurements
• Entropic information-disturbance tradeoff
• Towards a unified approach to information-disturbance tradeoffs in quantum measurements

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